# Computing Pareto-Optimal Transit Routes Through Mathematical Algorithms

by: M. Fawad Zazai and Armin Fugenschuh

**Abstract**

Afghanistan is geo-strategically in an important transit zone in South and Central Asia, but currently lacks of modern infrastructure. We present the construction of optimal transit routes in Afghanistan through mathematical optimization. Basically there are three different optimization goals a) the shortest route w.r.t. the distance, b) the cheapest route w.r.t. the construction cost, and c) the most convenient route w.r.t. the elevation change. It is possible to combine two objectives by considering the Pareto front. For the design and modeling of the routes, a computer program named “Contra” (Computing an Optimal Network of Transit Routes through mathematical Algorithms) was developed. As a demonstrator example, we compute Pareto-optimal routes between two Afghan cities.

**Keywords:**

Afghanistan, transit routes, shortest path problem, graph theory, Dijkstra’s algorithm, computational geometry.

link to material: http://ifors.org/wp-content/uploads/2017/11/AMOS62_ZazaiFuegenschuh_2017.pdf